Saturday, September 4, 2010

Tinkering With The Nash Equilibrium, Pt. II- Beyond Unexploitable Shoving

In the last post, we took a look at quite a few hands that were profitable to shove when heads up in the small blind.  I had also shown the hands with which it were profitable to defend against this play.  This time around, however, we will take a different tack and assume that we know that the big blind will be defending with the proper range against the unexploitable shove range.  Once again, we will use my favorite hypothetical example of a $2/4 game with 20BB stacks and a 5% rake and a defending hand range of 44+, A7o+, A3s+, KJo+, KTs+, QJs.  The simulation was run Monte Carlo style 10000k times.

Now here is what we can push:

The rabbit hole keeps getting deeper....  Notice that even after running the simulation 10 million times, there is still a tiny sampling error with 93s and assumedly the 53s as well, as neither J3s nor T3s are profitable and the 53s shows a minuscule $.01 profit, respectively.  Our unexploitable range has now grown from 38.4% of hands to an incredible 54.7%.

But why stop here?  Most players I play against simply refuse to make calls with hands like KTs, A3s, and QJs...even guys who I play against every day.  Let's run the simulation one more time with a more "typical" calling range of 55+, A8o+, A7s+, KJo+, KJs+.

86.4% of all hands are now playable.  In other words, all but the biggest of turds.  Oh?  What is that you say?  86.4% is not enough?  Ok then, let's toss a dead small blind into the pot and run it again and see what happens.

Happy now?  Yes, it's true.  With a typical calling range aided by the compensation of a dead small blind, you can now shove every single hand.  Naturally, logic dictates that you shouldn't be doing this.  While it would work a few times, it would quickly backfire and cause otherwise nitty players to begin playing more correctly against you and would thwart future attempts with a tighter shove range.  Besides, it's hardly optimal.  Rather, this was just an intellectual primer for the third and final installment of this series, where we finally combine all this knowledge to make you the ultimate motherfuckin' shortstack Houdini. 


Andu said...

I assume you play on cake network, how this play works with 30bb stacks?

Lorin Yelle said...

It does, but to a much lesser degree. At that point, however, the profits are meager and the play is too far from optimal to be even worthwhile, let alone the fact that the variance takes on a massive curve.

Rather, I play a normal game there until my stack dwindles down to about the 20BB mark and then I start shoving.

Matthew said...

This is interesting. I'm wondering how much your range changes if you say have 21 or 22 bbs. By the way, do you know any good forums for short stacking or a good place/thread for beginner short stacking? I'm having trouble finding good information. Your blog is one of few things I've come across. Thanks.

Lorin Yelle said...

Nah, you are stuck with me :)

Unless you are the rain man, figuring out the difference of 1-2 bbs would be too cumbersome to be practical. Also, picking up a few extra steals means that you would have to leave the table sooner, meaning you would have to sacrifice EV so I doubt it would even be worth it.

Almost all ssing advice you would find on the internet is highly suspect. Let me be clear about this so everyone can hear it: shortstackin' ain't easy. While there are many people out there who do it for a profit, I would wager everything I own that there are fewer than 100 people that earn enough to make a living in the First World. What can we take away from this? Too few people understand enough about it to accurately explain it in a functional way, so their treatises on it lack any quality information, despite their best intentions. Those who do understand it are not willing to share what they know.

I do because I play at Pokerworld where the buy in is 30 bb so most of the strategy is unusable there. However, I do offer coaching if you are interested.